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MathGroup Archive 2005

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Re: Using Select with arrays? (Relative newbie)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54234] Re: Using Select with arrays? (Relative newbie)
  • From: Curt Fischer <tentrillion at gmail.NOSPAM.com>
  • Date: Mon, 14 Feb 2005 00:57:50 -0500 (EST)
  • References: <cup5ip$dsr$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hugo Mallinson wrote:
> The subject might not be entirely correct, but here is my problem:
> 
> I have a list of 5-variable data points like
> 
> data = {
> {1, 1, string1, c, d}
> {1, 2, string2, c, d}
> {1, 3, string3, c, d}
> {1, 4, string4, c, d}
> {2, 1, string1, c, d}
> {2, 2, string2, c, d}
> {3, 1, string3, c, d}
> {4, 1, string2, c, d}
> {4, 2, string4, c, d}
> }
> 
> 
> and I want to extract just the points that have 1 (or 2, etc) as their 
> first value. I think I should do something like
> 
> Select[data, {1, _Integer, _String, _Integer, _Integer}]
> 
> but that doesn't work.

None of your data matches the pattern you made.  When you enter things 
like string2 or c or d into Mathematica without quotation marks, they 
are not strings or integers.  You can easily find out what Mathematica 
thinks they are.

In[1]:=
data = {{1, 1,
      string1, c, d} , {1, 2, string2, c, d}, {1, 3,
       string3, c, d}, {1, 4, string4, c, d} , {2, 1,
       string1, c, d}, {2, 2, string2, c, d}, {3, 1,
       string3, c, d} , {4, 1, string2, c, d}, {4, 2, string4, c, d}};

In[2]:=
Map[Head, data, {2}]
Out[2]=
{{Integer, Integer, Symbol, Symbol, Symbol}, {Integer, Integer, Symbol,
     Symbol, Symbol}, {
   Integer, Integer, Symbol, Symbol, Symbol}, {Integer, Integer, Symbol,
     Symbol, Symbol}, {
   Integer, Integer, Symbol, Symbol, Symbol}, {Integer, Integer, Symbol,
     Symbol, Symbol}, {
   Integer, Integer, Symbol, Symbol, Symbol}, {Integer, Integer, Symbol,
     Symbol, Symbol}, {Integer, Integer, Symbol, Symbol, Symbol}}

That is, they are all Symbols.  We can re-write your pattern to be more 
flexible and we can use Cases[] instead of Select[].  (IME Cases[] is 
easier to figure out.)

In[3]:=
Cases[data, {1, _Integer, _, _, _}]
Out[3]=
{{1, 1, string1, c, d}, {1, 2, string2, c, d}, {
   1, 3, string3, c, d}, {1, 4, string4, c, d}}

So that gets you the preliminary result.  But you want to extract the 
member of this list that has the maximal second element.

> Having done that I need to find the maximum value of #2 for each 
> string, which I presumably do by the same method as above to extract 
> all string1 (or ...2) and then use Map[] and Max[]. I would do this all 
> with For loops (revealing my lack of Mathematica chops :-) ) but I'd 
> really like to learn how to do this sort of extraction in a 
> Mathematica-y way. Any help would be greatly appreciated!

Let's say you want to know the maximum integer that occurs in slot #2 
for all of the data that contain string3.

In[4]:=
Max[Part[#,2]&/@Cases[data,{_Integer,_Integer, string3,_,_}]]

Out[4]=
3

This code extracts the second part from all of the list elements that 
match {_Integer, _Integer, string3, _,_} and finds the maximum value 
thereof.
-- 
Curt Fischer


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